Snaking of radial solutions of the multi-dimensional Swift-Hohenberg equation: A numerical study

被引:52
作者
McCalla, Scott [1 ]
Sandstede, Bjoern [1 ]
机构
[1] Brown Univ, Div Appl Math, Providence, RI 02912 USA
基金
美国国家科学基金会;
关键词
Swift-Hohenberg equation; Radial localized structures; Snaking; LOCALIZED STRUCTURES; PATTERNS; LADDERS; SNAKES;
D O I
10.1016/j.physd.2010.04.004
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The bifurcation structure of localized stationary radial patterns of the Swift-Hohenberg equation is explored when a continuous parameter n is varied that corresponds to the underlying space dimension whenever n is an integer. In particular, we investigate howl D pulses and 2-pulses are connected to planar spots and rings when n is increased from 1 to 2. We also elucidate changes in the snaking diagrams of spots when the dimension is switched from 2 to 3. (C) 2010 Elsevier B.V. All rights reserved.
引用
收藏
页码:1581 / 1592
页数:12
相关论文
共 24 条
  • [1] [Anonymous], 2006, Patterns and Interfaces in Dissipative Dynamics
  • [2] AVITABILE D, 2010, SNAKE NOT SNAKE PLAN
  • [3] SNAKES, LADDERS, AND ISOLAS OF LOCALIZED PATTERNS
    Beck, Margaret
    Knobloch, Juergen
    Lloyd, David J. B.
    Sandstede, Bjoern
    Wagenknecht, Thomas
    [J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2009, 41 (03) : 936 - 972
  • [4] Homoclinic snaking: Structure and stability
    Burke, John
    Knobloch, Edgar
    [J]. CHAOS, 2007, 17 (03)
  • [5] Localized states in the generalized Swift-Hohenberg equation
    Burke, John
    Knobloch, Edgar
    [J]. PHYSICAL REVIEW E, 2006, 73 (05):
  • [6] Snakes and ladders: Localized states in the Swift-Hohenberg equation
    Burke, John
    Knobloch, Edgar
    [J]. PHYSICS LETTERS A, 2007, 360 (06) : 681 - 688
  • [7] Exponential asymptotics of localised patterns and snaking bifurcation diagrams
    Chapman, S. J.
    Kozyreff, G.
    [J]. PHYSICA D-NONLINEAR PHENOMENA, 2009, 238 (03) : 319 - 354
  • [8] Stable static localized structures in one dimension
    Coullet, P
    Riera, C
    Tresser, C
    [J]. PHYSICAL REVIEW LETTERS, 2000, 84 (14) : 3069 - 3072
  • [9] PATTERN-FORMATION OUTSIDE OF EQUILIBRIUM
    CROSS, MC
    HOHENBERG, PC
    [J]. REVIEWS OF MODERN PHYSICS, 1993, 65 (03) : 851 - 1112
  • [10] DAWES JHP, PHILOS T R IN PRESS